Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,10,Mod(1,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(8.75560921479\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 1596x^{3} + 5754x^{2} + 488987x - 2711704 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(18.8209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 11.8209 | 0.522416 | 0.261208 | − | 0.965283i | \(-0.415879\pi\) | ||||
0.261208 | + | 0.965283i | \(0.415879\pi\) | |||||||
\(3\) | −67.6654 | −0.482304 | −0.241152 | − | 0.970487i | \(-0.577525\pi\) | ||||
−0.241152 | + | 0.970487i | \(0.577525\pi\) | |||||||
\(4\) | −372.266 | −0.727082 | ||||||||
\(5\) | 2390.67 | 1.71062 | 0.855311 | − | 0.518115i | \(-0.173366\pi\) | ||||
0.855311 | + | 0.518115i | \(0.173366\pi\) | |||||||
\(6\) | −799.867 | −0.251963 | ||||||||
\(7\) | −11355.8 | −1.78763 | −0.893814 | − | 0.448438i | \(-0.851980\pi\) | ||||
−0.893814 | + | 0.448438i | \(0.851980\pi\) | |||||||
\(8\) | −10452.8 | −0.902255 | ||||||||
\(9\) | −15104.4 | −0.767383 | ||||||||
\(10\) | 28259.9 | 0.893656 | ||||||||
\(11\) | −17740.6 | −0.365343 | −0.182672 | − | 0.983174i | \(-0.558475\pi\) | ||||
−0.182672 | + | 0.983174i | \(0.558475\pi\) | |||||||
\(12\) | 25189.5 | 0.350675 | ||||||||
\(13\) | −76108.0 | −0.739069 | −0.369535 | − | 0.929217i | \(-0.620483\pi\) | ||||
−0.369535 | + | 0.929217i | \(0.620483\pi\) | |||||||
\(14\) | −134236. | −0.933885 | ||||||||
\(15\) | −161765. | −0.825040 | ||||||||
\(16\) | 67038.0 | 0.255730 | ||||||||
\(17\) | −83521.0 | −0.242536 | ||||||||
\(18\) | −178548. | −0.400893 | ||||||||
\(19\) | 661811. | 1.16505 | 0.582523 | − | 0.812814i | \(-0.302066\pi\) | ||||
0.582523 | + | 0.812814i | \(0.302066\pi\) | |||||||
\(20\) | −889964. | −1.24376 | ||||||||
\(21\) | 768396. | 0.862180 | ||||||||
\(22\) | −209710. | −0.190861 | ||||||||
\(23\) | −1.64772e6 | −1.22774 | −0.613872 | − | 0.789405i | \(-0.710389\pi\) | ||||
−0.613872 | + | 0.789405i | \(0.710389\pi\) | |||||||
\(24\) | 707295. | 0.435161 | ||||||||
\(25\) | 3.76216e6 | 1.92623 | ||||||||
\(26\) | −899667. | −0.386102 | ||||||||
\(27\) | 2.35390e6 | 0.852416 | ||||||||
\(28\) | 4.22738e6 | 1.29975 | ||||||||
\(29\) | 1.49876e6 | 0.393496 | 0.196748 | − | 0.980454i | \(-0.436962\pi\) | ||||
0.196748 | + | 0.980454i | \(0.436962\pi\) | |||||||
\(30\) | −1.91222e6 | −0.431014 | ||||||||
\(31\) | −4.40242e6 | −0.856177 | −0.428089 | − | 0.903737i | \(-0.640813\pi\) | ||||
−0.428089 | + | 0.903737i | \(0.640813\pi\) | |||||||
\(32\) | 6.14430e6 | 1.03585 | ||||||||
\(33\) | 1.20042e6 | 0.176207 | ||||||||
\(34\) | −987295. | −0.126704 | ||||||||
\(35\) | −2.71480e7 | −3.05796 | ||||||||
\(36\) | 5.62285e6 | 0.557950 | ||||||||
\(37\) | −5.62188e6 | −0.493144 | −0.246572 | − | 0.969125i | \(-0.579304\pi\) | ||||
−0.246572 | + | 0.969125i | \(0.579304\pi\) | |||||||
\(38\) | 7.82322e6 | 0.608638 | ||||||||
\(39\) | 5.14988e6 | 0.356456 | ||||||||
\(40\) | −2.49892e7 | −1.54342 | ||||||||
\(41\) | 2.29725e7 | 1.26964 | 0.634821 | − | 0.772659i | \(-0.281074\pi\) | ||||
0.634821 | + | 0.772659i | \(0.281074\pi\) | |||||||
\(42\) | 9.08315e6 | 0.450417 | ||||||||
\(43\) | −7.92989e6 | −0.353720 | −0.176860 | − | 0.984236i | \(-0.556594\pi\) | ||||
−0.176860 | + | 0.984236i | \(0.556594\pi\) | |||||||
\(44\) | 6.60422e6 | 0.265634 | ||||||||
\(45\) | −3.61096e7 | −1.31270 | ||||||||
\(46\) | −1.94776e7 | −0.641393 | ||||||||
\(47\) | −5.69337e7 | −1.70188 | −0.850940 | − | 0.525262i | \(-0.823967\pi\) | ||||
−0.850940 | + | 0.525262i | \(0.823967\pi\) | |||||||
\(48\) | −4.53615e6 | −0.123339 | ||||||||
\(49\) | 8.86009e7 | 2.19561 | ||||||||
\(50\) | 4.44722e7 | 1.00629 | ||||||||
\(51\) | 5.65148e6 | 0.116976 | ||||||||
\(52\) | 2.83324e7 | 0.537364 | ||||||||
\(53\) | 2.56355e6 | 0.0446272 | 0.0223136 | − | 0.999751i | \(-0.492897\pi\) | ||||
0.0223136 | + | 0.999751i | \(0.492897\pi\) | |||||||
\(54\) | 2.78253e7 | 0.445316 | ||||||||
\(55\) | −4.24119e7 | −0.624964 | ||||||||
\(56\) | 1.18700e8 | 1.61290 | ||||||||
\(57\) | −4.47817e7 | −0.561906 | ||||||||
\(58\) | 1.77167e7 | 0.205569 | ||||||||
\(59\) | −6.87685e7 | −0.738849 | −0.369424 | − | 0.929261i | \(-0.620445\pi\) | ||||
−0.369424 | + | 0.929261i | \(0.620445\pi\) | |||||||
\(60\) | 6.02197e7 | 0.599872 | ||||||||
\(61\) | −1.09661e8 | −1.01407 | −0.507036 | − | 0.861925i | \(-0.669259\pi\) | ||||
−0.507036 | + | 0.861925i | \(0.669259\pi\) | |||||||
\(62\) | −5.20406e7 | −0.447280 | ||||||||
\(63\) | 1.71523e8 | 1.37179 | ||||||||
\(64\) | 3.83079e7 | 0.285416 | ||||||||
\(65\) | −1.81949e8 | −1.26427 | ||||||||
\(66\) | 1.41901e7 | 0.0920531 | ||||||||
\(67\) | 1.44824e8 | 0.878017 | 0.439008 | − | 0.898483i | \(-0.355330\pi\) | ||||
0.439008 | + | 0.898483i | \(0.355330\pi\) | |||||||
\(68\) | 3.10920e7 | 0.176343 | ||||||||
\(69\) | 1.11494e8 | 0.592147 | ||||||||
\(70\) | −3.20914e8 | −1.59752 | ||||||||
\(71\) | −6.07354e7 | −0.283648 | −0.141824 | − | 0.989892i | \(-0.545297\pi\) | ||||
−0.141824 | + | 0.989892i | \(0.545297\pi\) | |||||||
\(72\) | 1.57884e8 | 0.692375 | ||||||||
\(73\) | −1.68554e8 | −0.694684 | −0.347342 | − | 0.937739i | \(-0.612916\pi\) | ||||
−0.347342 | + | 0.937739i | \(0.612916\pi\) | |||||||
\(74\) | −6.64557e7 | −0.257626 | ||||||||
\(75\) | −2.54568e8 | −0.929027 | ||||||||
\(76\) | −2.46370e8 | −0.847083 | ||||||||
\(77\) | 2.01459e8 | 0.653098 | ||||||||
\(78\) | 6.08763e7 | 0.186218 | ||||||||
\(79\) | 1.00310e8 | 0.289749 | 0.144875 | − | 0.989450i | \(-0.453722\pi\) | ||||
0.144875 | + | 0.989450i | \(0.453722\pi\) | |||||||
\(80\) | 1.60265e8 | 0.437456 | ||||||||
\(81\) | 1.38022e8 | 0.356259 | ||||||||
\(82\) | 2.71557e8 | 0.663282 | ||||||||
\(83\) | −5.82713e8 | −1.34773 | −0.673865 | − | 0.738854i | \(-0.735367\pi\) | ||||
−0.673865 | + | 0.738854i | \(0.735367\pi\) | |||||||
\(84\) | −2.86048e8 | −0.626876 | ||||||||
\(85\) | −1.99671e8 | −0.414887 | ||||||||
\(86\) | −9.37386e7 | −0.184789 | ||||||||
\(87\) | −1.01414e8 | −0.189785 | ||||||||
\(88\) | 1.85440e8 | 0.329633 | ||||||||
\(89\) | −1.56066e7 | −0.0263665 | −0.0131832 | − | 0.999913i | \(-0.504196\pi\) | ||||
−0.0131832 | + | 0.999913i | \(0.504196\pi\) | |||||||
\(90\) | −4.26848e8 | −0.685776 | ||||||||
\(91\) | 8.64268e8 | 1.32118 | ||||||||
\(92\) | 6.13390e8 | 0.892671 | ||||||||
\(93\) | 2.97891e8 | 0.412938 | ||||||||
\(94\) | −6.73009e8 | −0.889089 | ||||||||
\(95\) | 1.58217e9 | 1.99295 | ||||||||
\(96\) | −4.15757e8 | −0.499596 | ||||||||
\(97\) | 1.64798e9 | 1.89008 | 0.945040 | − | 0.326956i | \(-0.106023\pi\) | ||||
0.945040 | + | 0.326956i | \(0.106023\pi\) | |||||||
\(98\) | 1.04734e9 | 1.14702 | ||||||||
\(99\) | 2.67961e8 | 0.280358 | ||||||||
\(100\) | −1.40052e9 | −1.40052 | ||||||||
\(101\) | −9.32619e8 | −0.891780 | −0.445890 | − | 0.895088i | \(-0.647113\pi\) | ||||
−0.445890 | + | 0.895088i | \(0.647113\pi\) | |||||||
\(102\) | 6.68057e7 | 0.0611101 | ||||||||
\(103\) | −1.88493e9 | −1.65017 | −0.825085 | − | 0.565009i | \(-0.808873\pi\) | ||||
−0.825085 | + | 0.565009i | \(0.808873\pi\) | |||||||
\(104\) | 7.95544e8 | 0.666829 | ||||||||
\(105\) | 1.83698e9 | 1.47486 | ||||||||
\(106\) | 3.03035e7 | 0.0233140 | ||||||||
\(107\) | −9.44012e7 | −0.0696226 | −0.0348113 | − | 0.999394i | \(-0.511083\pi\) | ||||
−0.0348113 | + | 0.999394i | \(0.511083\pi\) | |||||||
\(108\) | −8.76278e8 | −0.619776 | ||||||||
\(109\) | −1.72481e9 | −1.17037 | −0.585183 | − | 0.810901i | \(-0.698977\pi\) | ||||
−0.585183 | + | 0.810901i | \(0.698977\pi\) | |||||||
\(110\) | −5.01347e8 | −0.326491 | ||||||||
\(111\) | 3.80406e8 | 0.237845 | ||||||||
\(112\) | −7.61271e8 | −0.457149 | ||||||||
\(113\) | 1.02688e9 | 0.592471 | 0.296235 | − | 0.955115i | \(-0.404269\pi\) | ||||
0.296235 | + | 0.955115i | \(0.404269\pi\) | |||||||
\(114\) | −5.29361e8 | −0.293549 | ||||||||
\(115\) | −3.93915e9 | −2.10021 | ||||||||
\(116\) | −5.57936e8 | −0.286104 | ||||||||
\(117\) | 1.14957e9 | 0.567149 | ||||||||
\(118\) | −8.12907e8 | −0.385986 | ||||||||
\(119\) | 9.48449e8 | 0.433563 | ||||||||
\(120\) | 1.69091e9 | 0.744396 | ||||||||
\(121\) | −2.04322e9 | −0.866524 | ||||||||
\(122\) | −1.29630e9 | −0.529767 | ||||||||
\(123\) | −1.55445e9 | −0.612354 | ||||||||
\(124\) | 1.63887e9 | 0.622511 | ||||||||
\(125\) | 4.32481e9 | 1.58442 | ||||||||
\(126\) | 2.02756e9 | 0.716647 | ||||||||
\(127\) | 2.57593e9 | 0.878653 | 0.439327 | − | 0.898327i | \(-0.355217\pi\) | ||||
0.439327 | + | 0.898327i | \(0.355217\pi\) | |||||||
\(128\) | −2.69305e9 | −0.886746 | ||||||||
\(129\) | 5.36579e8 | 0.170600 | ||||||||
\(130\) | −2.15080e9 | −0.660474 | ||||||||
\(131\) | −1.67438e9 | −0.496746 | −0.248373 | − | 0.968664i | \(-0.579896\pi\) | ||||
−0.248373 | + | 0.968664i | \(0.579896\pi\) | |||||||
\(132\) | −4.46877e8 | −0.128117 | ||||||||
\(133\) | −7.51540e9 | −2.08267 | ||||||||
\(134\) | 1.71195e9 | 0.458690 | ||||||||
\(135\) | 5.62740e9 | 1.45816 | ||||||||
\(136\) | 8.73031e8 | 0.218829 | ||||||||
\(137\) | 9.77626e8 | 0.237099 | 0.118550 | − | 0.992948i | \(-0.462176\pi\) | ||||
0.118550 | + | 0.992948i | \(0.462176\pi\) | |||||||
\(138\) | 1.31796e9 | 0.309347 | ||||||||
\(139\) | −5.07318e8 | −0.115269 | −0.0576346 | − | 0.998338i | \(-0.518356\pi\) | ||||
−0.0576346 | + | 0.998338i | \(0.518356\pi\) | |||||||
\(140\) | 1.01063e10 | 2.22338 | ||||||||
\(141\) | 3.85244e9 | 0.820824 | ||||||||
\(142\) | −7.17948e8 | −0.148182 | ||||||||
\(143\) | 1.35020e9 | 0.270014 | ||||||||
\(144\) | −1.01257e9 | −0.196242 | ||||||||
\(145\) | 3.58303e9 | 0.673123 | ||||||||
\(146\) | −1.99247e9 | −0.362914 | ||||||||
\(147\) | −5.99522e9 | −1.05895 | ||||||||
\(148\) | 2.09283e9 | 0.358556 | ||||||||
\(149\) | −3.39357e9 | −0.564052 | −0.282026 | − | 0.959407i | \(-0.591006\pi\) | ||||
−0.282026 | + | 0.959407i | \(0.591006\pi\) | |||||||
\(150\) | −3.00923e9 | −0.485339 | ||||||||
\(151\) | 2.54210e9 | 0.397921 | 0.198961 | − | 0.980007i | \(-0.436243\pi\) | ||||
0.198961 | + | 0.980007i | \(0.436243\pi\) | |||||||
\(152\) | −6.91780e9 | −1.05117 | ||||||||
\(153\) | 1.26153e9 | 0.186118 | ||||||||
\(154\) | 2.38143e9 | 0.341189 | ||||||||
\(155\) | −1.05247e10 | −1.46460 | ||||||||
\(156\) | −1.91712e9 | −0.259173 | ||||||||
\(157\) | −8.59628e9 | −1.12918 | −0.564588 | − | 0.825373i | \(-0.690965\pi\) | ||||
−0.564588 | + | 0.825373i | \(0.690965\pi\) | |||||||
\(158\) | 1.18576e9 | 0.151370 | ||||||||
\(159\) | −1.73464e8 | −0.0215239 | ||||||||
\(160\) | 1.46890e10 | 1.77195 | ||||||||
\(161\) | 1.87112e10 | 2.19475 | ||||||||
\(162\) | 1.63155e9 | 0.186115 | ||||||||
\(163\) | 7.22903e8 | 0.0802113 | 0.0401057 | − | 0.999195i | \(-0.487231\pi\) | ||||
0.0401057 | + | 0.999195i | \(0.487231\pi\) | |||||||
\(164\) | −8.55189e9 | −0.923134 | ||||||||
\(165\) | 2.86982e9 | 0.301423 | ||||||||
\(166\) | −6.88820e9 | −0.704076 | ||||||||
\(167\) | 5.77488e9 | 0.574538 | 0.287269 | − | 0.957850i | \(-0.407253\pi\) | ||||
0.287269 | + | 0.957850i | \(0.407253\pi\) | |||||||
\(168\) | −8.03192e9 | −0.777906 | ||||||||
\(169\) | −4.81207e9 | −0.453776 | ||||||||
\(170\) | −2.36029e9 | −0.216743 | ||||||||
\(171\) | −9.99625e9 | −0.894036 | ||||||||
\(172\) | 2.95203e9 | 0.257183 | ||||||||
\(173\) | −2.26224e9 | −0.192014 | −0.0960068 | − | 0.995381i | \(-0.530607\pi\) | ||||
−0.0960068 | + | 0.995381i | \(0.530607\pi\) | |||||||
\(174\) | −1.19881e9 | −0.0991466 | ||||||||
\(175\) | −4.27224e10 | −3.44338 | ||||||||
\(176\) | −1.18929e9 | −0.0934291 | ||||||||
\(177\) | 4.65325e9 | 0.356350 | ||||||||
\(178\) | −1.84484e8 | −0.0137743 | ||||||||
\(179\) | −3.69322e9 | −0.268885 | −0.134443 | − | 0.990921i | \(-0.542924\pi\) | ||||
−0.134443 | + | 0.990921i | \(0.542924\pi\) | |||||||
\(180\) | 1.34424e10 | 0.954441 | ||||||||
\(181\) | 1.91251e10 | 1.32449 | 0.662247 | − | 0.749285i | \(-0.269603\pi\) | ||||
0.662247 | + | 0.749285i | \(0.269603\pi\) | |||||||
\(182\) | 1.02164e10 | 0.690206 | ||||||||
\(183\) | 7.42027e9 | 0.489091 | ||||||||
\(184\) | 1.72233e10 | 1.10774 | ||||||||
\(185\) | −1.34400e10 | −0.843582 | ||||||||
\(186\) | 3.52135e9 | 0.215725 | ||||||||
\(187\) | 1.48171e9 | 0.0886088 | ||||||||
\(188\) | 2.11945e10 | 1.23741 | ||||||||
\(189\) | −2.67305e10 | −1.52380 | ||||||||
\(190\) | 1.87027e10 | 1.04115 | ||||||||
\(191\) | −4.41416e9 | −0.239993 | −0.119996 | − | 0.992774i | \(-0.538288\pi\) | ||||
−0.119996 | + | 0.992774i | \(0.538288\pi\) | |||||||
\(192\) | −2.59212e9 | −0.137657 | ||||||||
\(193\) | −5.98467e9 | −0.310479 | −0.155239 | − | 0.987877i | \(-0.549615\pi\) | ||||
−0.155239 | + | 0.987877i | \(0.549615\pi\) | |||||||
\(194\) | 1.94807e10 | 0.987407 | ||||||||
\(195\) | 1.23116e10 | 0.609762 | ||||||||
\(196\) | −3.29831e10 | −1.59639 | ||||||||
\(197\) | 2.74494e10 | 1.29848 | 0.649240 | − | 0.760584i | \(-0.275087\pi\) | ||||
0.649240 | + | 0.760584i | \(0.275087\pi\) | |||||||
\(198\) | 3.16754e9 | 0.146463 | ||||||||
\(199\) | 3.34164e10 | 1.51050 | 0.755250 | − | 0.655436i | \(-0.227515\pi\) | ||||
0.755250 | + | 0.655436i | \(0.227515\pi\) | |||||||
\(200\) | −3.93253e10 | −1.73795 | ||||||||
\(201\) | −9.79955e9 | −0.423471 | ||||||||
\(202\) | −1.10244e10 | −0.465880 | ||||||||
\(203\) | −1.70196e10 | −0.703425 | ||||||||
\(204\) | −2.10385e9 | −0.0850511 | ||||||||
\(205\) | 5.49197e10 | 2.17188 | ||||||||
\(206\) | −2.22817e10 | −0.862075 | ||||||||
\(207\) | 2.48878e10 | 0.942150 | ||||||||
\(208\) | −5.10212e9 | −0.189002 | ||||||||
\(209\) | −1.17409e10 | −0.425641 | ||||||||
\(210\) | 2.17148e10 | 0.770493 | ||||||||
\(211\) | 4.50084e9 | 0.156323 | 0.0781615 | − | 0.996941i | \(-0.475095\pi\) | ||||
0.0781615 | + | 0.996941i | \(0.475095\pi\) | |||||||
\(212\) | −9.54321e8 | −0.0324477 | ||||||||
\(213\) | 4.10969e9 | 0.136805 | ||||||||
\(214\) | −1.11591e9 | −0.0363720 | ||||||||
\(215\) | −1.89577e10 | −0.605081 | ||||||||
\(216\) | −2.46050e10 | −0.769097 | ||||||||
\(217\) | 4.99930e10 | 1.53053 | ||||||||
\(218\) | −2.03888e10 | −0.611418 | ||||||||
\(219\) | 1.14053e10 | 0.335049 | ||||||||
\(220\) | 1.57885e10 | 0.454400 | ||||||||
\(221\) | 6.35662e9 | 0.179251 | ||||||||
\(222\) | 4.49675e9 | 0.124254 | ||||||||
\(223\) | −4.59996e10 | −1.24561 | −0.622805 | − | 0.782377i | \(-0.714007\pi\) | ||||
−0.622805 | + | 0.782377i | \(0.714007\pi\) | |||||||
\(224\) | −6.97736e10 | −1.85172 | ||||||||
\(225\) | −5.68252e10 | −1.47815 | ||||||||
\(226\) | 1.21387e10 | 0.309516 | ||||||||
\(227\) | 1.68405e10 | 0.420958 | 0.210479 | − | 0.977598i | \(-0.432498\pi\) | ||||
0.210479 | + | 0.977598i | \(0.432498\pi\) | |||||||
\(228\) | 1.66707e10 | 0.408552 | ||||||||
\(229\) | 4.54814e10 | 1.09288 | 0.546442 | − | 0.837497i | \(-0.315982\pi\) | ||||
0.546442 | + | 0.837497i | \(0.315982\pi\) | |||||||
\(230\) | −4.65644e10 | −1.09718 | ||||||||
\(231\) | −1.36318e10 | −0.314992 | ||||||||
\(232\) | −1.56663e10 | −0.355034 | ||||||||
\(233\) | −5.00961e10 | −1.11353 | −0.556766 | − | 0.830669i | \(-0.687958\pi\) | ||||
−0.556766 | + | 0.830669i | \(0.687958\pi\) | |||||||
\(234\) | 1.35889e10 | 0.296288 | ||||||||
\(235\) | −1.36110e11 | −2.91127 | ||||||||
\(236\) | 2.56002e10 | 0.537204 | ||||||||
\(237\) | −6.78751e9 | −0.139747 | ||||||||
\(238\) | 1.12115e10 | 0.226500 | ||||||||
\(239\) | 4.75443e10 | 0.942558 | 0.471279 | − | 0.881984i | \(-0.343792\pi\) | ||||
0.471279 | + | 0.881984i | \(0.343792\pi\) | |||||||
\(240\) | −1.08444e10 | −0.210987 | ||||||||
\(241\) | 8.24645e10 | 1.57467 | 0.787337 | − | 0.616523i | \(-0.211459\pi\) | ||||
0.787337 | + | 0.616523i | \(0.211459\pi\) | |||||||
\(242\) | −2.41527e10 | −0.452686 | ||||||||
\(243\) | −5.56712e10 | −1.02424 | ||||||||
\(244\) | 4.08231e10 | 0.737313 | ||||||||
\(245\) | 2.11815e11 | 3.75586 | ||||||||
\(246\) | −1.83750e10 | −0.319903 | ||||||||
\(247\) | −5.03691e10 | −0.861049 | ||||||||
\(248\) | 4.60177e10 | 0.772490 | ||||||||
\(249\) | 3.94295e10 | 0.650016 | ||||||||
\(250\) | 5.11232e10 | 0.827728 | ||||||||
\(251\) | −5.90523e10 | −0.939085 | −0.469543 | − | 0.882910i | \(-0.655581\pi\) | ||||
−0.469543 | + | 0.882910i | \(0.655581\pi\) | |||||||
\(252\) | −6.38520e10 | −0.997407 | ||||||||
\(253\) | 2.92315e10 | 0.448548 | ||||||||
\(254\) | 3.04499e10 | 0.459022 | ||||||||
\(255\) | 1.35108e10 | 0.200102 | ||||||||
\(256\) | −5.14479e10 | −0.748666 | ||||||||
\(257\) | 3.35982e10 | 0.480415 | 0.240207 | − | 0.970722i | \(-0.422785\pi\) | ||||
0.240207 | + | 0.970722i | \(0.422785\pi\) | |||||||
\(258\) | 6.34286e9 | 0.0891244 | ||||||||
\(259\) | 6.38410e10 | 0.881557 | ||||||||
\(260\) | 6.77333e10 | 0.919226 | ||||||||
\(261\) | −2.26378e10 | −0.301962 | ||||||||
\(262\) | −1.97928e10 | −0.259508 | ||||||||
\(263\) | 3.91693e9 | 0.0504830 | 0.0252415 | − | 0.999681i | \(-0.491965\pi\) | ||||
0.0252415 | + | 0.999681i | \(0.491965\pi\) | |||||||
\(264\) | −1.25478e10 | −0.158983 | ||||||||
\(265\) | 6.12859e9 | 0.0763403 | ||||||||
\(266\) | −8.88390e10 | −1.08802 | ||||||||
\(267\) | 1.05602e9 | 0.0127167 | ||||||||
\(268\) | −5.39129e10 | −0.638390 | ||||||||
\(269\) | 6.33897e10 | 0.738131 | 0.369065 | − | 0.929403i | \(-0.379678\pi\) | ||||
0.369065 | + | 0.929403i | \(0.379678\pi\) | |||||||
\(270\) | 6.65210e10 | 0.761767 | ||||||||
\(271\) | 4.27576e10 | 0.481561 | 0.240781 | − | 0.970580i | \(-0.422597\pi\) | ||||
0.240781 | + | 0.970580i | \(0.422597\pi\) | |||||||
\(272\) | −5.59908e9 | −0.0620235 | ||||||||
\(273\) | −5.84811e10 | −0.637211 | ||||||||
\(274\) | 1.15564e10 | 0.123864 | ||||||||
\(275\) | −6.67430e10 | −0.703734 | ||||||||
\(276\) | −4.15053e10 | −0.430539 | ||||||||
\(277\) | −1.32848e11 | −1.35580 | −0.677899 | − | 0.735155i | \(-0.737109\pi\) | ||||
−0.677899 | + | 0.735155i | \(0.737109\pi\) | |||||||
\(278\) | −5.99696e9 | −0.0602185 | ||||||||
\(279\) | 6.64958e10 | 0.657015 | ||||||||
\(280\) | 2.83773e11 | 2.75905 | ||||||||
\(281\) | −1.43951e11 | −1.37733 | −0.688663 | − | 0.725082i | \(-0.741802\pi\) | ||||
−0.688663 | + | 0.725082i | \(0.741802\pi\) | |||||||
\(282\) | 4.55394e10 | 0.428812 | ||||||||
\(283\) | 6.72871e10 | 0.623581 | 0.311790 | − | 0.950151i | \(-0.399071\pi\) | ||||
0.311790 | + | 0.950151i | \(0.399071\pi\) | |||||||
\(284\) | 2.26097e10 | 0.206235 | ||||||||
\(285\) | −1.07058e11 | −0.961209 | ||||||||
\(286\) | 1.59606e10 | 0.141060 | ||||||||
\(287\) | −2.60872e11 | −2.26965 | ||||||||
\(288\) | −9.28060e10 | −0.794895 | ||||||||
\(289\) | 6.97576e9 | 0.0588235 | ||||||||
\(290\) | 4.23547e10 | 0.351650 | ||||||||
\(291\) | −1.11511e11 | −0.911593 | ||||||||
\(292\) | 6.27470e10 | 0.505092 | ||||||||
\(293\) | 8.76124e10 | 0.694482 | 0.347241 | − | 0.937776i | \(-0.387119\pi\) | ||||
0.347241 | + | 0.937776i | \(0.387119\pi\) | |||||||
\(294\) | −7.08690e10 | −0.553214 | ||||||||
\(295\) | −1.64403e11 | −1.26389 | ||||||||
\(296\) | 5.87645e10 | 0.444941 | ||||||||
\(297\) | −4.17596e10 | −0.311424 | ||||||||
\(298\) | −4.01152e10 | −0.294670 | ||||||||
\(299\) | 1.25405e11 | 0.907389 | ||||||||
\(300\) | 9.47671e10 | 0.675479 | ||||||||
\(301\) | 9.00504e10 | 0.632319 | ||||||||
\(302\) | 3.00500e10 | 0.207880 | ||||||||
\(303\) | 6.31060e10 | 0.430109 | ||||||||
\(304\) | 4.43665e10 | 0.297936 | ||||||||
\(305\) | −2.62163e11 | −1.73469 | ||||||||
\(306\) | 1.49125e10 | 0.0972308 | ||||||||
\(307\) | 2.30476e11 | 1.48083 | 0.740413 | − | 0.672153i | \(-0.234630\pi\) | ||||
0.740413 | + | 0.672153i | \(0.234630\pi\) | |||||||
\(308\) | −7.49963e10 | −0.474855 | ||||||||
\(309\) | 1.27545e11 | 0.795884 | ||||||||
\(310\) | −1.24412e11 | −0.765128 | ||||||||
\(311\) | 2.89033e10 | 0.175197 | 0.0875984 | − | 0.996156i | \(-0.472081\pi\) | ||||
0.0875984 | + | 0.996156i | \(0.472081\pi\) | |||||||
\(312\) | −5.38308e10 | −0.321614 | ||||||||
\(313\) | −2.95929e11 | −1.74276 | −0.871382 | − | 0.490605i | \(-0.836776\pi\) | ||||
−0.871382 | + | 0.490605i | \(0.836776\pi\) | |||||||
\(314\) | −1.01616e11 | −0.589900 | ||||||||
\(315\) | 4.10054e11 | 2.34662 | ||||||||
\(316\) | −3.73420e10 | −0.210671 | ||||||||
\(317\) | −3.12812e11 | −1.73987 | −0.869934 | − | 0.493168i | \(-0.835839\pi\) | ||||
−0.869934 | + | 0.493168i | \(0.835839\pi\) | |||||||
\(318\) | −2.05050e9 | −0.0112444 | ||||||||
\(319\) | −2.65888e10 | −0.143761 | ||||||||
\(320\) | 9.15814e10 | 0.488239 | ||||||||
\(321\) | 6.38769e9 | 0.0335793 | ||||||||
\(322\) | 2.21184e11 | 1.14657 | ||||||||
\(323\) | −5.52751e10 | −0.282565 | ||||||||
\(324\) | −5.13809e10 | −0.259029 | ||||||||
\(325\) | −2.86331e11 | −1.42362 | ||||||||
\(326\) | 8.54537e9 | 0.0419037 | ||||||||
\(327\) | 1.16710e11 | 0.564473 | ||||||||
\(328\) | −2.40128e11 | −1.14554 | ||||||||
\(329\) | 6.46529e11 | 3.04233 | ||||||||
\(330\) | 3.39239e10 | 0.157468 | ||||||||
\(331\) | 8.91016e9 | 0.0408000 | 0.0204000 | − | 0.999792i | \(-0.493506\pi\) | ||||
0.0204000 | + | 0.999792i | \(0.493506\pi\) | |||||||
\(332\) | 2.16924e11 | 0.979910 | ||||||||
\(333\) | 8.49150e10 | 0.378430 | ||||||||
\(334\) | 6.82644e10 | 0.300148 | ||||||||
\(335\) | 3.46225e11 | 1.50195 | ||||||||
\(336\) | 5.15117e10 | 0.220485 | ||||||||
\(337\) | 2.90899e10 | 0.122859 | 0.0614296 | − | 0.998111i | \(-0.480434\pi\) | ||||
0.0614296 | + | 0.998111i | \(0.480434\pi\) | |||||||
\(338\) | −5.68831e10 | −0.237060 | ||||||||
\(339\) | −6.94843e10 | −0.285751 | ||||||||
\(340\) | 7.43306e10 | 0.301657 | ||||||||
\(341\) | 7.81015e10 | 0.312799 | ||||||||
\(342\) | −1.18165e11 | −0.467058 | ||||||||
\(343\) | −5.47888e11 | −2.13731 | ||||||||
\(344\) | 8.28899e10 | 0.319145 | ||||||||
\(345\) | 2.66544e11 | 1.01294 | ||||||||
\(346\) | −2.67418e10 | −0.100311 | ||||||||
\(347\) | 1.09628e11 | 0.405918 | 0.202959 | − | 0.979187i | \(-0.434944\pi\) | ||||
0.202959 | + | 0.979187i | \(0.434944\pi\) | |||||||
\(348\) | 3.77530e10 | 0.137989 | ||||||||
\(349\) | −6.35598e10 | −0.229334 | −0.114667 | − | 0.993404i | \(-0.536580\pi\) | ||||
−0.114667 | + | 0.993404i | \(0.536580\pi\) | |||||||
\(350\) | −5.05018e11 | −1.79887 | ||||||||
\(351\) | −1.79151e11 | −0.629995 | ||||||||
\(352\) | −1.09004e11 | −0.378442 | ||||||||
\(353\) | 7.79401e10 | 0.267162 | 0.133581 | − | 0.991038i | \(-0.457352\pi\) | ||||
0.133581 | + | 0.991038i | \(0.457352\pi\) | |||||||
\(354\) | 5.50057e10 | 0.186163 | ||||||||
\(355\) | −1.45198e11 | −0.485214 | ||||||||
\(356\) | 5.80979e9 | 0.0191706 | ||||||||
\(357\) | −6.41772e10 | −0.209109 | ||||||||
\(358\) | −4.36573e10 | −0.140470 | ||||||||
\(359\) | 3.06852e11 | 0.974998 | 0.487499 | − | 0.873124i | \(-0.337909\pi\) | ||||
0.487499 | + | 0.873124i | \(0.337909\pi\) | |||||||
\(360\) | 3.77447e11 | 1.18439 | ||||||||
\(361\) | 1.15306e11 | 0.357331 | ||||||||
\(362\) | 2.26076e11 | 0.691937 | ||||||||
\(363\) | 1.38255e11 | 0.417928 | ||||||||
\(364\) | −3.21738e11 | −0.960607 | ||||||||
\(365\) | −4.02957e11 | −1.18834 | ||||||||
\(366\) | 8.77144e10 | 0.255509 | ||||||||
\(367\) | −2.13117e11 | −0.613225 | −0.306613 | − | 0.951834i | \(-0.599196\pi\) | ||||
−0.306613 | + | 0.951834i | \(0.599196\pi\) | |||||||
\(368\) | −1.10460e11 | −0.313971 | ||||||||
\(369\) | −3.46986e11 | −0.974302 | ||||||||
\(370\) | −1.58874e11 | −0.440701 | ||||||||
\(371\) | −2.91112e10 | −0.0797769 | ||||||||
\(372\) | −1.10895e11 | −0.300240 | ||||||||
\(373\) | 2.27081e11 | 0.607423 | 0.303712 | − | 0.952764i | \(-0.401774\pi\) | ||||
0.303712 | + | 0.952764i | \(0.401774\pi\) | |||||||
\(374\) | 1.75152e10 | 0.0462906 | ||||||||
\(375\) | −2.92640e11 | −0.764175 | ||||||||
\(376\) | 5.95119e11 | 1.53553 | ||||||||
\(377\) | −1.14067e11 | −0.290821 | ||||||||
\(378\) | −3.15979e11 | −0.796059 | ||||||||
\(379\) | 3.53633e11 | 0.880391 | 0.440196 | − | 0.897902i | \(-0.354909\pi\) | ||||
0.440196 | + | 0.897902i | \(0.354909\pi\) | |||||||
\(380\) | −5.88988e11 | −1.44904 | ||||||||
\(381\) | −1.74301e11 | −0.423778 | ||||||||
\(382\) | −5.21794e10 | −0.125376 | ||||||||
\(383\) | −6.69512e11 | −1.58988 | −0.794939 | − | 0.606689i | \(-0.792497\pi\) | ||||
−0.794939 | + | 0.606689i | \(0.792497\pi\) | |||||||
\(384\) | 1.82226e11 | 0.427681 | ||||||||
\(385\) | 4.81621e11 | 1.11720 | ||||||||
\(386\) | −7.07443e10 | −0.162199 | ||||||||
\(387\) | 1.19776e11 | 0.271438 | ||||||||
\(388\) | −6.13488e11 | −1.37424 | ||||||||
\(389\) | 6.62054e11 | 1.46595 | 0.732976 | − | 0.680254i | \(-0.238131\pi\) | ||||
0.732976 | + | 0.680254i | \(0.238131\pi\) | |||||||
\(390\) | 1.45535e11 | 0.318549 | ||||||||
\(391\) | 1.37619e11 | 0.297772 | ||||||||
\(392\) | −9.26131e11 | −1.98100 | ||||||||
\(393\) | 1.13298e11 | 0.239583 | ||||||||
\(394\) | 3.24477e11 | 0.678346 | ||||||||
\(395\) | 2.39808e11 | 0.495651 | ||||||||
\(396\) | −9.97527e10 | −0.203843 | ||||||||
\(397\) | −6.61102e11 | −1.33571 | −0.667854 | − | 0.744293i | \(-0.732787\pi\) | ||||
−0.667854 | + | 0.744293i | \(0.732787\pi\) | |||||||
\(398\) | 3.95013e11 | 0.789110 | ||||||||
\(399\) | 5.08533e11 | 1.00448 | ||||||||
\(400\) | 2.52208e11 | 0.492593 | ||||||||
\(401\) | 6.56727e11 | 1.26834 | 0.634169 | − | 0.773195i | \(-0.281342\pi\) | ||||
0.634169 | + | 0.773195i | \(0.281342\pi\) | |||||||
\(402\) | −1.15840e11 | −0.221228 | ||||||||
\(403\) | 3.35059e11 | 0.632774 | ||||||||
\(404\) | 3.47182e11 | 0.648397 | ||||||||
\(405\) | 3.29964e11 | 0.609424 | ||||||||
\(406\) | −2.01187e11 | −0.367480 | ||||||||
\(407\) | 9.97354e10 | 0.180167 | ||||||||
\(408\) | −5.90740e10 | −0.105542 | ||||||||
\(409\) | −4.36145e11 | −0.770684 | −0.385342 | − | 0.922774i | \(-0.625917\pi\) | ||||
−0.385342 | + | 0.922774i | \(0.625917\pi\) | |||||||
\(410\) | 6.49201e11 | 1.13462 | ||||||||
\(411\) | −6.61515e10 | −0.114354 | ||||||||
\(412\) | 7.01697e11 | 1.19981 | ||||||||
\(413\) | 7.80923e11 | 1.32079 | ||||||||
\(414\) | 2.94197e11 | 0.492194 | ||||||||
\(415\) | −1.39307e12 | −2.30546 | ||||||||
\(416\) | −4.67631e11 | −0.765566 | ||||||||
\(417\) | 3.43279e10 | 0.0555948 | ||||||||
\(418\) | −1.38789e11 | −0.222362 | ||||||||
\(419\) | 6.66344e11 | 1.05617 | 0.528087 | − | 0.849190i | \(-0.322909\pi\) | ||||
0.528087 | + | 0.849190i | \(0.322909\pi\) | |||||||
\(420\) | −6.83844e11 | −1.07235 | ||||||||
\(421\) | −4.68417e11 | −0.726713 | −0.363357 | − | 0.931650i | \(-0.618369\pi\) | ||||
−0.363357 | + | 0.931650i | \(0.618369\pi\) | |||||||
\(422\) | 5.32041e10 | 0.0816656 | ||||||||
\(423\) | 8.59949e11 | 1.30599 | ||||||||
\(424\) | −2.67964e10 | −0.0402651 | ||||||||
\(425\) | −3.14220e11 | −0.467179 | ||||||||
\(426\) | 4.85803e10 | 0.0714688 | ||||||||
\(427\) | 1.24529e12 | 1.81278 | ||||||||
\(428\) | 3.51423e10 | 0.0506213 | ||||||||
\(429\) | −9.13619e10 | −0.130229 | ||||||||
\(430\) | −2.24098e11 | −0.316104 | ||||||||
\(431\) | −3.43298e11 | −0.479207 | −0.239604 | − | 0.970871i | \(-0.577018\pi\) | ||||
−0.239604 | + | 0.970871i | \(0.577018\pi\) | |||||||
\(432\) | 1.57801e11 | 0.217988 | ||||||||
\(433\) | −1.30884e12 | −1.78933 | −0.894666 | − | 0.446735i | \(-0.852587\pi\) | ||||
−0.894666 | + | 0.446735i | \(0.852587\pi\) | |||||||
\(434\) | 5.90964e11 | 0.799571 | ||||||||
\(435\) | −2.42447e11 | −0.324650 | ||||||||
\(436\) | 6.42088e11 | 0.850952 | ||||||||
\(437\) | −1.09048e12 | −1.43038 | ||||||||
\(438\) | 1.34821e11 | 0.175035 | ||||||||
\(439\) | 5.48226e11 | 0.704481 | 0.352241 | − | 0.935909i | \(-0.385420\pi\) | ||||
0.352241 | + | 0.935909i | \(0.385420\pi\) | |||||||
\(440\) | 4.43324e11 | 0.563877 | ||||||||
\(441\) | −1.33826e12 | −1.68488 | ||||||||
\(442\) | 7.51411e10 | 0.0936434 | ||||||||
\(443\) | −1.00051e10 | −0.0123426 | −0.00617130 | − | 0.999981i | \(-0.501964\pi\) | ||||
−0.00617130 | + | 0.999981i | \(0.501964\pi\) | |||||||
\(444\) | −1.41612e11 | −0.172933 | ||||||||
\(445\) | −3.73101e10 | −0.0451031 | ||||||||
\(446\) | −5.43758e11 | −0.650727 | ||||||||
\(447\) | 2.29628e11 | 0.272045 | ||||||||
\(448\) | −4.35017e11 | −0.510218 | ||||||||
\(449\) | −8.97323e10 | −0.104193 | −0.0520967 | − | 0.998642i | \(-0.516590\pi\) | ||||
−0.0520967 | + | 0.998642i | \(0.516590\pi\) | |||||||
\(450\) | −6.71726e11 | −0.772211 | ||||||||
\(451\) | −4.07546e11 | −0.463855 | ||||||||
\(452\) | −3.82272e11 | −0.430775 | ||||||||
\(453\) | −1.72012e11 | −0.191919 | ||||||||
\(454\) | 1.99071e11 | 0.219915 | ||||||||
\(455\) | 2.06618e12 | 2.26004 | ||||||||
\(456\) | 4.68096e11 | 0.506983 | ||||||||
\(457\) | −1.13166e12 | −1.21365 | −0.606823 | − | 0.794837i | \(-0.707556\pi\) | ||||
−0.606823 | + | 0.794837i | \(0.707556\pi\) | |||||||
\(458\) | 5.37632e11 | 0.570940 | ||||||||
\(459\) | −1.96600e11 | −0.206741 | ||||||||
\(460\) | 1.46641e12 | 1.52702 | ||||||||
\(461\) | −1.76123e12 | −1.81620 | −0.908098 | − | 0.418757i | \(-0.862466\pi\) | ||||
−0.908098 | + | 0.418757i | \(0.862466\pi\) | |||||||
\(462\) | −1.61140e11 | −0.164557 | ||||||||
\(463\) | −6.00361e11 | −0.607152 | −0.303576 | − | 0.952807i | \(-0.598181\pi\) | ||||
−0.303576 | + | 0.952807i | \(0.598181\pi\) | |||||||
\(464\) | 1.00474e11 | 0.100629 | ||||||||
\(465\) | 7.12159e11 | 0.706380 | ||||||||
\(466\) | −5.92182e11 | −0.581727 | ||||||||
\(467\) | −7.30949e11 | −0.711150 | −0.355575 | − | 0.934648i | \(-0.615715\pi\) | ||||
−0.355575 | + | 0.934648i | \(0.615715\pi\) | |||||||
\(468\) | −4.27944e11 | −0.412364 | ||||||||
\(469\) | −1.64459e12 | −1.56957 | ||||||||
\(470\) | −1.60894e12 | −1.52090 | ||||||||
\(471\) | 5.81671e11 | 0.544607 | ||||||||
\(472\) | 7.18826e11 | 0.666630 | ||||||||
\(473\) | 1.40681e11 | 0.129229 | ||||||||
\(474\) | −8.02347e10 | −0.0730062 | ||||||||
\(475\) | 2.48984e12 | 2.24414 | ||||||||
\(476\) | −3.53075e11 | −0.315236 | ||||||||
\(477\) | −3.87208e10 | −0.0342462 | ||||||||
\(478\) | 5.62018e11 | 0.492407 | ||||||||
\(479\) | −1.76035e12 | −1.52788 | −0.763938 | − | 0.645289i | \(-0.776737\pi\) | ||||
−0.763938 | + | 0.645289i | \(0.776737\pi\) | |||||||
\(480\) | −9.93936e11 | −0.854619 | ||||||||
\(481\) | 4.27870e11 | 0.364467 | ||||||||
\(482\) | 9.74807e11 | 0.822634 | ||||||||
\(483\) | −1.26610e12 | −1.05854 | ||||||||
\(484\) | 7.60621e11 | 0.630034 | ||||||||
\(485\) | 3.93978e12 | 3.23321 | ||||||||
\(486\) | −6.58085e11 | −0.535080 | ||||||||
\(487\) | 2.40112e12 | 1.93434 | 0.967171 | − | 0.254126i | \(-0.0817878\pi\) | ||||
0.967171 | + | 0.254126i | \(0.0817878\pi\) | |||||||
\(488\) | 1.14627e12 | 0.914951 | ||||||||
\(489\) | −4.89155e10 | −0.0386862 | ||||||||
\(490\) | 2.50385e12 | 1.96212 | ||||||||
\(491\) | −3.93654e11 | −0.305666 | −0.152833 | − | 0.988252i | \(-0.548840\pi\) | ||||
−0.152833 | + | 0.988252i | \(0.548840\pi\) | |||||||
\(492\) | 5.78667e11 | 0.445231 | ||||||||
\(493\) | −1.25178e11 | −0.0954368 | ||||||||
\(494\) | −5.95409e11 | −0.449826 | ||||||||
\(495\) | 6.40605e11 | 0.479587 | ||||||||
\(496\) | −2.95129e11 | −0.218950 | ||||||||
\(497\) | 6.89700e11 | 0.507057 | ||||||||
\(498\) | 4.66093e11 | 0.339579 | ||||||||
\(499\) | −1.16585e12 | −0.841763 | −0.420881 | − | 0.907116i | \(-0.638279\pi\) | ||||
−0.420881 | + | 0.907116i | \(0.638279\pi\) | |||||||
\(500\) | −1.60998e12 | −1.15201 | ||||||||
\(501\) | −3.90760e11 | −0.277102 | ||||||||
\(502\) | −6.98053e11 | −0.490593 | ||||||||
\(503\) | −1.06497e12 | −0.741794 | −0.370897 | − | 0.928674i | \(-0.620950\pi\) | ||||
−0.370897 | + | 0.928674i | \(0.620950\pi\) | |||||||
\(504\) | −1.79290e12 | −1.23771 | ||||||||
\(505\) | −2.22958e12 | −1.52550 | ||||||||
\(506\) | 3.45544e11 | 0.234329 | ||||||||
\(507\) | 3.25611e11 | 0.218858 | ||||||||
\(508\) | −9.58931e11 | −0.638853 | ||||||||
\(509\) | −1.27920e12 | −0.844711 | −0.422355 | − | 0.906430i | \(-0.638797\pi\) | ||||
−0.422355 | + | 0.906430i | \(0.638797\pi\) | |||||||
\(510\) | 1.59710e11 | 0.104536 | ||||||||
\(511\) | 1.91407e12 | 1.24184 | ||||||||
\(512\) | 7.70679e11 | 0.495631 | ||||||||
\(513\) | 1.55784e12 | 0.993103 | ||||||||
\(514\) | 3.97161e11 | 0.250976 | ||||||||
\(515\) | −4.50625e12 | −2.82282 | ||||||||
\(516\) | −1.99750e11 | −0.124041 | ||||||||
\(517\) | 1.01004e12 | 0.621771 | ||||||||
\(518\) | 7.54659e11 | 0.460540 | ||||||||
\(519\) | 1.53076e11 | 0.0926089 | ||||||||
\(520\) | 1.90188e12 | 1.14069 | ||||||||
\(521\) | 1.01572e12 | 0.603955 | 0.301977 | − | 0.953315i | \(-0.402353\pi\) | ||||
0.301977 | + | 0.953315i | \(0.402353\pi\) | |||||||
\(522\) | −2.67600e11 | −0.157750 | ||||||||
\(523\) | −7.26782e10 | −0.0424763 | −0.0212381 | − | 0.999774i | \(-0.506761\pi\) | ||||
−0.0212381 | + | 0.999774i | \(0.506761\pi\) | |||||||
\(524\) | 6.23316e11 | 0.361175 | ||||||||
\(525\) | 2.89083e12 | 1.66076 | ||||||||
\(526\) | 4.63017e10 | 0.0263731 | ||||||||
\(527\) | 3.67694e11 | 0.207653 | ||||||||
\(528\) | 8.04740e10 | 0.0450612 | ||||||||
\(529\) | 9.13829e11 | 0.507358 | ||||||||
\(530\) | 7.24456e10 | 0.0398814 | ||||||||
\(531\) | 1.03871e12 | 0.566980 | ||||||||
\(532\) | 2.79773e12 | 1.51427 | ||||||||
\(533\) | −1.74839e12 | −0.938354 | ||||||||
\(534\) | 1.24832e10 | 0.00664339 | ||||||||
\(535\) | −2.25682e11 | −0.119098 | ||||||||
\(536\) | −1.51382e12 | −0.792195 | ||||||||
\(537\) | 2.49903e11 | 0.129684 | ||||||||
\(538\) | 7.49324e11 | 0.385611 | ||||||||
\(539\) | −1.57183e12 | −0.802153 | ||||||||
\(540\) | −2.09489e12 | −1.06020 | ||||||||
\(541\) | −4.64227e11 | −0.232993 | −0.116496 | − | 0.993191i | \(-0.537166\pi\) | ||||
−0.116496 | + | 0.993191i | \(0.537166\pi\) | |||||||
\(542\) | 5.05434e11 | 0.251575 | ||||||||
\(543\) | −1.29411e12 | −0.638809 | ||||||||
\(544\) | −5.13178e11 | −0.251231 | ||||||||
\(545\) | −4.12345e12 | −2.00205 | ||||||||
\(546\) | −6.91300e11 | −0.332889 | ||||||||
\(547\) | −2.64589e12 | −1.26366 | −0.631828 | − | 0.775109i | \(-0.717695\pi\) | ||||
−0.631828 | + | 0.775109i | \(0.717695\pi\) | |||||||
\(548\) | −3.63937e11 | −0.172391 | ||||||||
\(549\) | 1.65637e12 | 0.778181 | ||||||||
\(550\) | −7.88964e11 | −0.367642 | ||||||||
\(551\) | 9.91894e11 | 0.458441 | ||||||||
\(552\) | −1.16542e12 | −0.534267 | ||||||||
\(553\) | −1.13910e12 | −0.517964 | ||||||||
\(554\) | −1.57038e12 | −0.708291 | ||||||||
\(555\) | 9.09425e11 | 0.406863 | ||||||||
\(556\) | 1.88857e11 | 0.0838101 | ||||||||
\(557\) | −1.89427e11 | −0.0833862 | −0.0416931 | − | 0.999130i | \(-0.513275\pi\) | ||||
−0.0416931 | + | 0.999130i | \(0.513275\pi\) | |||||||
\(558\) | 7.86042e11 | 0.343235 | ||||||||
\(559\) | 6.03528e11 | 0.261423 | ||||||||
\(560\) | −1.81994e12 | −0.782009 | ||||||||
\(561\) | −1.00261e11 | −0.0427364 | ||||||||
\(562\) | −1.70163e12 | −0.719537 | ||||||||
\(563\) | 3.50385e12 | 1.46980 | 0.734900 | − | 0.678175i | \(-0.237229\pi\) | ||||
0.734900 | + | 0.678175i | \(0.237229\pi\) | |||||||
\(564\) | −1.43413e12 | −0.596806 | ||||||||
\(565\) | 2.45493e12 | 1.01349 | ||||||||
\(566\) | 7.95395e11 | 0.325769 | ||||||||
\(567\) | −1.56735e12 | −0.636858 | ||||||||
\(568\) | 6.34857e11 | 0.255923 | ||||||||
\(569\) | 4.15736e12 | 1.66270 | 0.831348 | − | 0.555752i | \(-0.187570\pi\) | ||||
0.831348 | + | 0.555752i | \(0.187570\pi\) | |||||||
\(570\) | −1.26553e12 | −0.502151 | ||||||||
\(571\) | 3.38832e12 | 1.33390 | 0.666948 | − | 0.745104i | \(-0.267600\pi\) | ||||
0.666948 | + | 0.745104i | \(0.267600\pi\) | |||||||
\(572\) | −5.02634e11 | −0.196322 | ||||||||
\(573\) | 2.98686e11 | 0.115749 | ||||||||
\(574\) | −3.08375e12 | −1.18570 | ||||||||
\(575\) | −6.19899e12 | −2.36492 | ||||||||
\(576\) | −5.78617e11 | −0.219023 | ||||||||
\(577\) | −7.93761e11 | −0.298125 | −0.149062 | − | 0.988828i | \(-0.547626\pi\) | ||||
−0.149062 | + | 0.988828i | \(0.547626\pi\) | |||||||
\(578\) | 8.24599e10 | 0.0307303 | ||||||||
\(579\) | 4.04955e11 | 0.149745 | ||||||||
\(580\) | −1.33384e12 | −0.489415 | ||||||||
\(581\) | 6.61718e12 | 2.40924 | ||||||||
\(582\) | −1.31817e12 | −0.476231 | ||||||||
\(583\) | −4.54789e10 | −0.0163043 | ||||||||
\(584\) | 1.76187e12 | 0.626782 | ||||||||
\(585\) | 2.74823e12 | 0.970178 | ||||||||
\(586\) | 1.03566e12 | 0.362809 | ||||||||
\(587\) | 3.50948e12 | 1.22003 | 0.610016 | − | 0.792389i | \(-0.291163\pi\) | ||||
0.610016 | + | 0.792389i | \(0.291163\pi\) | |||||||
\(588\) | 2.23181e12 | 0.769946 | ||||||||
\(589\) | −2.91357e12 | −0.997485 | ||||||||
\(590\) | −1.94339e12 | −0.660277 | ||||||||
\(591\) | −1.85738e12 | −0.626262 | ||||||||
\(592\) | −3.76879e11 | −0.126111 | ||||||||
\(593\) | 1.01035e12 | 0.335527 | 0.167763 | − | 0.985827i | \(-0.446346\pi\) | ||||
0.167763 | + | 0.985827i | \(0.446346\pi\) | |||||||
\(594\) | −4.93637e11 | −0.162693 | ||||||||
\(595\) | 2.26743e12 | 0.741663 | ||||||||
\(596\) | 1.26331e12 | 0.410112 | ||||||||
\(597\) | −2.26114e12 | −0.728521 | ||||||||
\(598\) | 1.48240e12 | 0.474034 | ||||||||
\(599\) | 1.26453e12 | 0.401337 | 0.200669 | − | 0.979659i | \(-0.435689\pi\) | ||||
0.200669 | + | 0.979659i | \(0.435689\pi\) | |||||||
\(600\) | 2.66096e12 | 0.838220 | ||||||||
\(601\) | 4.11286e12 | 1.28591 | 0.642953 | − | 0.765906i | \(-0.277709\pi\) | ||||
0.642953 | + | 0.765906i | \(0.277709\pi\) | |||||||
\(602\) | 1.06448e12 | 0.330334 | ||||||||
\(603\) | −2.18747e12 | −0.673775 | ||||||||
\(604\) | −9.46338e11 | −0.289321 | ||||||||
\(605\) | −4.88466e12 | −1.48230 | ||||||||
\(606\) | 7.45971e11 | 0.224696 | ||||||||
\(607\) | 2.94970e12 | 0.881919 | 0.440959 | − | 0.897527i | \(-0.354638\pi\) | ||||
0.440959 | + | 0.897527i | \(0.354638\pi\) | |||||||
\(608\) | 4.06637e12 | 1.20681 | ||||||||
\(609\) | 1.15164e12 | 0.339265 | ||||||||
\(610\) | −3.09901e12 | −0.906232 | ||||||||
\(611\) | 4.33311e12 | 1.25781 | ||||||||
\(612\) | −4.69626e11 | −0.135323 | ||||||||
\(613\) | −1.04819e12 | −0.299825 | −0.149912 | − | 0.988699i | \(-0.547899\pi\) | ||||
−0.149912 | + | 0.988699i | \(0.547899\pi\) | |||||||
\(614\) | 2.72444e12 | 0.773606 | ||||||||
\(615\) | −3.71616e12 | −1.04751 | ||||||||
\(616\) | −2.10582e12 | −0.589261 | ||||||||
\(617\) | −2.24197e12 | −0.622797 | −0.311398 | − | 0.950279i | \(-0.600797\pi\) | ||||
−0.311398 | + | 0.950279i | \(0.600797\pi\) | |||||||
\(618\) | 1.50770e12 | 0.415782 | ||||||||
\(619\) | −4.31403e12 | −1.18107 | −0.590534 | − | 0.807013i | \(-0.701083\pi\) | ||||
−0.590534 | + | 0.807013i | \(0.701083\pi\) | |||||||
\(620\) | 3.91799e12 | 1.06488 | ||||||||
\(621\) | −3.87857e12 | −1.04655 | ||||||||
\(622\) | 3.41664e11 | 0.0915256 | ||||||||
\(623\) | 1.77225e11 | 0.0471335 | ||||||||
\(624\) | 3.45237e11 | 0.0911564 | ||||||||
\(625\) | 2.99120e12 | 0.784124 | ||||||||
\(626\) | −3.49816e12 | −0.910448 | ||||||||
\(627\) | 7.94454e11 | 0.205289 | ||||||||
\(628\) | 3.20010e12 | 0.821004 | ||||||||
\(629\) | 4.69545e11 | 0.119605 | ||||||||
\(630\) | 4.84721e12 | 1.22591 | ||||||||
\(631\) | −5.04376e12 | −1.26655 | −0.633275 | − | 0.773927i | \(-0.718290\pi\) | ||||
−0.633275 | + | 0.773927i | \(0.718290\pi\) | |||||||
\(632\) | −1.04852e12 | −0.261428 | ||||||||
\(633\) | −3.04552e11 | −0.0753953 | ||||||||
\(634\) | −3.69772e12 | −0.908934 | ||||||||
\(635\) | 6.15819e12 | 1.50304 | ||||||||
\(636\) | 6.45745e10 | 0.0156496 | ||||||||
\(637\) | −6.74324e12 | −1.62271 | ||||||||
\(638\) | −3.14305e11 | −0.0751031 | ||||||||
\(639\) | 9.17371e11 | 0.217666 | ||||||||
\(640\) | −6.43818e12 | −1.51689 | ||||||||
\(641\) | 4.31567e12 | 1.00969 | 0.504844 | − | 0.863210i | \(-0.331550\pi\) | ||||
0.504844 | + | 0.863210i | \(0.331550\pi\) | |||||||
\(642\) | 7.55084e10 | 0.0175423 | ||||||||
\(643\) | −4.67632e12 | −1.07883 | −0.539417 | − | 0.842039i | \(-0.681355\pi\) | ||||
−0.539417 | + | 0.842039i | \(0.681355\pi\) | |||||||
\(644\) | −6.96554e12 | −1.59576 | ||||||||
\(645\) | 1.28278e12 | 0.291833 | ||||||||
\(646\) | −6.53403e11 | −0.147616 | ||||||||
\(647\) | −2.41143e11 | −0.0541010 | −0.0270505 | − | 0.999634i | \(-0.508611\pi\) | ||||
−0.0270505 | + | 0.999634i | \(0.508611\pi\) | |||||||
\(648\) | −1.44272e12 | −0.321436 | ||||||||
\(649\) | 1.21999e12 | 0.269933 | ||||||||
\(650\) | −3.38469e12 | −0.743719 | ||||||||
\(651\) | −3.38280e12 | −0.738179 | ||||||||
\(652\) | −2.69112e11 | −0.0583202 | ||||||||
\(653\) | 5.60932e12 | 1.20726 | 0.603631 | − | 0.797264i | \(-0.293720\pi\) | ||||
0.603631 | + | 0.797264i | \(0.293720\pi\) | |||||||
\(654\) | 1.37962e12 | 0.294890 | ||||||||
\(655\) | −4.00289e12 | −0.849744 | ||||||||
\(656\) | 1.54003e12 | 0.324685 | ||||||||
\(657\) | 2.54591e12 | 0.533088 | ||||||||
\(658\) | 7.64256e12 | 1.58936 | ||||||||
\(659\) | −5.89433e12 | −1.21745 | −0.608724 | − | 0.793382i | \(-0.708318\pi\) | ||||
−0.608724 | + | 0.793382i | \(0.708318\pi\) | |||||||
\(660\) | −1.06833e12 | −0.219159 | ||||||||
\(661\) | −6.88972e11 | −0.140377 | −0.0701883 | − | 0.997534i | \(-0.522360\pi\) | ||||
−0.0701883 | + | 0.997534i | \(0.522360\pi\) | |||||||
\(662\) | 1.05326e11 | 0.0213145 | ||||||||
\(663\) | −4.30123e11 | −0.0864533 | ||||||||
\(664\) | 6.09100e12 | 1.21600 | ||||||||
\(665\) | −1.79668e13 | −3.56266 | ||||||||
\(666\) | 1.00377e12 | 0.197698 | ||||||||
\(667\) | −2.46953e12 | −0.483113 | ||||||||
\(668\) | −2.14979e12 | −0.417736 | ||||||||
\(669\) | 3.11258e12 | 0.600763 | ||||||||
\(670\) | 4.09270e12 | 0.784645 | ||||||||
\(671\) | 1.94546e12 | 0.370484 | ||||||||
\(672\) | 4.72126e12 | 0.893091 | ||||||||
\(673\) | 5.91814e12 | 1.11203 | 0.556016 | − | 0.831171i | \(-0.312329\pi\) | ||||
0.556016 | + | 0.831171i | \(0.312329\pi\) | |||||||
\(674\) | 3.43869e11 | 0.0641836 | ||||||||
\(675\) | 8.85577e12 | 1.64195 | ||||||||
\(676\) | 1.79137e12 | 0.329933 | ||||||||
\(677\) | 9.75918e12 | 1.78552 | 0.892759 | − | 0.450534i | \(-0.148766\pi\) | ||||
0.892759 | + | 0.450534i | \(0.148766\pi\) | |||||||
\(678\) | −8.21368e11 | −0.149281 | ||||||||
\(679\) | −1.87142e13 | −3.37876 | ||||||||
\(680\) | 2.08713e12 | 0.374334 | ||||||||
\(681\) | −1.13952e12 | −0.203030 | ||||||||
\(682\) | 9.23232e11 | 0.163411 | ||||||||
\(683\) | −1.05702e12 | −0.185862 | −0.0929310 | − | 0.995673i | \(-0.529624\pi\) | ||||
−0.0929310 | + | 0.995673i | \(0.529624\pi\) | |||||||
\(684\) | 3.72126e12 | 0.650037 | ||||||||
\(685\) | 2.33718e12 | 0.405587 | ||||||||
\(686\) | −6.47654e12 | −1.11657 | ||||||||
\(687\) | −3.07752e12 | −0.527103 | ||||||||
\(688\) | −5.31604e11 | −0.0904566 | ||||||||
\(689\) | −1.95107e11 | −0.0329826 | ||||||||
\(690\) | 3.15080e12 | 0.529175 | ||||||||
\(691\) | −1.03154e12 | −0.172122 | −0.0860608 | − | 0.996290i | \(-0.527428\pi\) | ||||
−0.0860608 | + | 0.996290i | \(0.527428\pi\) | |||||||
\(692\) | 8.42156e11 | 0.139610 | ||||||||
\(693\) | −3.04291e12 | −0.501176 | ||||||||
\(694\) | 1.29590e12 | 0.212058 | ||||||||
\(695\) | −1.21283e12 | −0.197182 | ||||||||
\(696\) | 1.06006e12 | 0.171234 | ||||||||
\(697\) | −1.91869e12 | −0.307934 | ||||||||
\(698\) | −7.51336e11 | −0.119808 | ||||||||
\(699\) | 3.38978e12 | 0.537061 | ||||||||
\(700\) | 1.59041e13 | 2.50362 | ||||||||
\(701\) | 5.14597e12 | 0.804889 | 0.402444 | − | 0.915444i | \(-0.368161\pi\) | ||||
0.402444 | + | 0.915444i | \(0.368161\pi\) | |||||||
\(702\) | −2.11773e12 | −0.329119 | ||||||||
\(703\) | −3.72062e12 | −0.574535 | ||||||||
\(704\) | −6.79605e11 | −0.104275 | ||||||||
\(705\) | 9.20991e12 | 1.40412 | ||||||||
\(706\) | 9.21324e11 | 0.139570 | ||||||||
\(707\) | 1.05906e13 | 1.59417 | ||||||||
\(708\) | −1.73225e12 | −0.259096 | ||||||||
\(709\) | −1.28349e13 | −1.90759 | −0.953795 | − | 0.300458i | \(-0.902861\pi\) | ||||
−0.953795 | + | 0.300458i | \(0.902861\pi\) | |||||||
\(710\) | −1.71638e12 | −0.253483 | ||||||||
\(711\) | −1.51512e12 | −0.222348 | ||||||||
\(712\) | 1.63133e11 | 0.0237893 | ||||||||
\(713\) | 7.25395e12 | 1.05117 | ||||||||
\(714\) | −7.58633e11 | −0.109242 | ||||||||
\(715\) | 3.22788e12 | 0.461892 | ||||||||
\(716\) | 1.37486e12 | 0.195501 | ||||||||
\(717\) | −3.21711e12 | −0.454600 | ||||||||
\(718\) | 3.62727e12 | 0.509354 | ||||||||
\(719\) | −6.51717e12 | −0.909451 | −0.454725 | − | 0.890632i | \(-0.650263\pi\) | ||||
−0.454725 | + | 0.890632i | \(0.650263\pi\) | |||||||
\(720\) | −2.42071e12 | −0.335697 | ||||||||
\(721\) | 2.14050e13 | 2.94989 | ||||||||
\(722\) | 1.36303e12 | 0.186675 | ||||||||
\(723\) | −5.58000e12 | −0.759472 | ||||||||
\(724\) | −7.11962e12 | −0.963016 | ||||||||
\(725\) | 5.63857e12 | 0.757963 | ||||||||
\(726\) | 1.63430e12 | 0.218332 | ||||||||
\(727\) | −4.75481e12 | −0.631290 | −0.315645 | − | 0.948877i | \(-0.602221\pi\) | ||||
−0.315645 | + | 0.948877i | \(0.602221\pi\) | |||||||
\(728\) | −9.03406e12 | −1.19204 | ||||||||
\(729\) | 1.05033e12 | 0.137737 | ||||||||
\(730\) | −4.76333e12 | −0.620808 | ||||||||
\(731\) | 6.62313e11 | 0.0857896 | ||||||||
\(732\) | −2.76231e12 | −0.355609 | ||||||||
\(733\) | −4.70068e12 | −0.601441 | −0.300721 | − | 0.953712i | \(-0.597227\pi\) | ||||
−0.300721 | + | 0.953712i | \(0.597227\pi\) | |||||||
\(734\) | −2.51923e12 | −0.320358 | ||||||||
\(735\) | −1.43326e13 | −1.81147 | ||||||||
\(736\) | −1.01241e13 | −1.27176 | ||||||||
\(737\) | −2.56926e12 | −0.320778 | ||||||||
\(738\) | −4.10170e12 | −0.508991 | ||||||||
\(739\) | 7.68600e12 | 0.947983 | 0.473992 | − | 0.880529i | \(-0.342813\pi\) | ||||
0.473992 | + | 0.880529i | \(0.342813\pi\) | |||||||
\(740\) | 5.00326e12 | 0.613353 | ||||||||
\(741\) | 3.40825e12 | 0.415288 | ||||||||
\(742\) | −3.44121e11 | −0.0416767 | ||||||||
\(743\) | 1.54208e13 | 1.85634 | 0.928170 | − | 0.372156i | \(-0.121382\pi\) | ||||
0.928170 | + | 0.372156i | \(0.121382\pi\) | |||||||
\(744\) | −3.11381e12 | −0.372575 | ||||||||
\(745\) | −8.11290e12 | −0.964879 | ||||||||
\(746\) | 2.68431e12 | 0.317328 | ||||||||
\(747\) | 8.80152e12 | 1.03423 | ||||||||
\(748\) | −5.51591e11 | −0.0644258 | ||||||||
\(749\) | 1.07200e12 | 0.124459 | ||||||||
\(750\) | −3.45927e12 | −0.399217 | ||||||||
\(751\) | −6.56715e12 | −0.753351 | −0.376676 | − | 0.926345i | \(-0.622933\pi\) | ||||
−0.376676 | + | 0.926345i | \(0.622933\pi\) | |||||||
\(752\) | −3.81672e12 | −0.435221 | ||||||||
\(753\) | 3.99580e12 | 0.452925 | ||||||||
\(754\) | −1.34838e12 | −0.151929 | ||||||||
\(755\) | 6.07732e12 | 0.680693 | ||||||||
\(756\) | 9.95085e12 | 1.10793 | ||||||||
\(757\) | −1.40433e13 | −1.55431 | −0.777156 | − | 0.629308i | \(-0.783338\pi\) | ||||
−0.777156 | + | 0.629308i | \(0.783338\pi\) | |||||||
\(758\) | 4.18026e12 | 0.459930 | ||||||||
\(759\) | −1.97796e12 | −0.216337 | ||||||||
\(760\) | −1.65382e13 | −1.79815 | ||||||||
\(761\) | −9.41842e12 | −1.01800 | −0.508999 | − | 0.860767i | \(-0.669984\pi\) | ||||
−0.508999 | + | 0.860767i | \(0.669984\pi\) | |||||||
\(762\) | −2.06040e12 | −0.221388 | ||||||||
\(763\) | 1.95866e13 | 2.09218 | ||||||||
\(764\) | 1.64324e12 | 0.174494 | ||||||||
\(765\) | 3.01591e12 | 0.318377 | ||||||||
\(766\) | −7.91425e12 | −0.830578 | ||||||||
\(767\) | 5.23384e12 | 0.546061 | ||||||||
\(768\) | 3.48125e12 | 0.361085 | ||||||||
\(769\) | 1.32235e13 | 1.36358 | 0.681788 | − | 0.731550i | \(-0.261203\pi\) | ||||
0.681788 | + | 0.731550i | \(0.261203\pi\) | |||||||
\(770\) | 5.69321e12 | 0.583645 | ||||||||
\(771\) | −2.27343e12 | −0.231706 | ||||||||
\(772\) | 2.22789e12 | 0.225744 | ||||||||
\(773\) | −1.14561e13 | −1.15406 | −0.577031 | − | 0.816722i | \(-0.695789\pi\) | ||||
−0.577031 | + | 0.816722i | \(0.695789\pi\) | |||||||
\(774\) | 1.41587e12 | 0.141804 | ||||||||
\(775\) | −1.65626e13 | −1.64919 | ||||||||
\(776\) | −1.72261e13 | −1.70533 | ||||||||
\(777\) | −4.31983e12 | −0.425179 | ||||||||
\(778\) | 7.82608e12 | 0.765837 | ||||||||
\(779\) | 1.52035e13 | 1.47919 | ||||||||
\(780\) | −4.58320e12 | −0.443347 | ||||||||
\(781\) | 1.07748e12 | 0.103629 | ||||||||
\(782\) | 1.62679e12 | 0.155561 | ||||||||
\(783\) | 3.52793e12 | 0.335422 | ||||||||
\(784\) | 5.93962e12 | 0.561483 | ||||||||
\(785\) | −2.05508e13 | −1.93159 | ||||||||
\(786\) | 1.33929e12 | 0.125162 | ||||||||
\(787\) | 4.46778e12 | 0.415151 | 0.207575 | − | 0.978219i | \(-0.433443\pi\) | ||||
0.207575 | + | 0.978219i | \(0.433443\pi\) | |||||||
\(788\) | −1.02185e13 | −0.944101 | ||||||||
\(789\) | −2.65041e11 | −0.0243482 | ||||||||
\(790\) | 2.83475e12 | 0.258936 | ||||||||
\(791\) | −1.16611e13 | −1.05912 | ||||||||
\(792\) | −2.80095e12 | −0.252954 | ||||||||
\(793\) | 8.34610e12 | 0.749470 | ||||||||
\(794\) | −7.81484e12 | −0.697795 | ||||||||
\(795\) | −4.14694e11 | −0.0368193 | ||||||||
\(796\) | −1.24398e13 | −1.09826 | ||||||||
\(797\) | −1.13816e13 | −0.999177 | −0.499589 | − | 0.866263i | \(-0.666515\pi\) | ||||
−0.499589 | + | 0.866263i | \(0.666515\pi\) | |||||||
\(798\) | 6.01133e12 | 0.524756 | ||||||||
\(799\) | 4.75516e12 | 0.412767 | ||||||||
\(800\) | 2.31159e13 | 1.99529 | ||||||||
\(801\) | 2.35728e11 | 0.0202332 | ||||||||
\(802\) | 7.76311e12 | 0.662600 | ||||||||
\(803\) | 2.99026e12 | 0.253798 | ||||||||
\(804\) | 3.64804e12 | 0.307898 | ||||||||
\(805\) | 4.47323e13 | 3.75439 | ||||||||
\(806\) | 3.96071e12 | 0.330571 | ||||||||
\(807\) | −4.28929e12 | −0.356003 | ||||||||
\(808\) | 9.74851e12 | 0.804613 | ||||||||
\(809\) | −1.94386e13 | −1.59550 | −0.797748 | − | 0.602991i | \(-0.793976\pi\) | ||||
−0.797748 | + | 0.602991i | \(0.793976\pi\) | |||||||
\(810\) | 3.90048e12 | 0.318373 | ||||||||
\(811\) | 1.02059e12 | 0.0828431 | 0.0414216 | − | 0.999142i | \(-0.486811\pi\) | ||||
0.0414216 | + | 0.999142i | \(0.486811\pi\) | |||||||
\(812\) | 6.33582e12 | 0.511447 | ||||||||
\(813\) | −2.89321e12 | −0.232259 | ||||||||
\(814\) | 1.17896e12 | 0.0941219 | ||||||||
\(815\) | 1.72822e12 | 0.137211 | ||||||||
\(816\) | 3.78864e11 | 0.0299142 | ||||||||
\(817\) | −5.24809e12 | −0.412099 | ||||||||
\(818\) | −5.15564e12 | −0.402618 | ||||||||
\(819\) | −1.30542e13 | −1.01385 | ||||||||
\(820\) | −2.04447e13 | −1.57913 | ||||||||
\(821\) | 2.88205e12 | 0.221390 | 0.110695 | − | 0.993854i | \(-0.464692\pi\) | ||||
0.110695 | + | 0.993854i | \(0.464692\pi\) | |||||||
\(822\) | −7.81971e11 | −0.0597403 | ||||||||
\(823\) | 1.16904e13 | 0.888237 | 0.444118 | − | 0.895968i | \(-0.353517\pi\) | ||||
0.444118 | + | 0.895968i | \(0.353517\pi\) | |||||||
\(824\) | 1.97029e13 | 1.48887 | ||||||||
\(825\) | 4.51619e12 | 0.339414 | ||||||||
\(826\) | 9.23122e12 | 0.690000 | ||||||||
\(827\) | 5.81279e12 | 0.432126 | 0.216063 | − | 0.976379i | \(-0.430678\pi\) | ||||
0.216063 | + | 0.976379i | \(0.430678\pi\) | |||||||
\(828\) | −9.26488e12 | −0.685020 | ||||||||
\(829\) | 6.40775e12 | 0.471205 | 0.235603 | − | 0.971849i | \(-0.424294\pi\) | ||||
0.235603 | + | 0.971849i | \(0.424294\pi\) | |||||||
\(830\) | −1.64674e13 | −1.20441 | ||||||||
\(831\) | 8.98920e12 | 0.653907 | ||||||||
\(832\) | −2.91554e12 | −0.210942 | ||||||||
\(833\) | −7.40004e12 | −0.532514 | ||||||||
\(834\) | 4.05787e11 | 0.0290436 | ||||||||
\(835\) | 1.38058e13 | 0.982817 | ||||||||
\(836\) | 4.37074e12 | 0.309476 | ||||||||
\(837\) | −1.03629e13 | −0.729819 | ||||||||
\(838\) | 7.87680e12 | 0.551762 | ||||||||
\(839\) | −3.65270e12 | −0.254498 | −0.127249 | − | 0.991871i | \(-0.540615\pi\) | ||||
−0.127249 | + | 0.991871i | \(0.540615\pi\) | |||||||
\(840\) | −1.92016e13 | −1.33070 | ||||||||
\(841\) | −1.22609e13 | −0.845161 | ||||||||
\(842\) | −5.53712e12 | −0.379647 | ||||||||
\(843\) | 9.74051e12 | 0.664290 | ||||||||
\(844\) | −1.67551e12 | −0.113660 | ||||||||
\(845\) | −1.15041e13 | −0.776240 | ||||||||
\(846\) | 1.01654e13 | 0.682272 | ||||||||
\(847\) | 2.32024e13 | 1.54902 | ||||||||
\(848\) | 1.71855e11 | 0.0114125 | ||||||||
\(849\) | −4.55301e12 | −0.300756 | ||||||||
\(850\) | −3.71436e12 | −0.244062 | ||||||||
\(851\) | 9.26328e12 | 0.605455 | ||||||||
\(852\) | −1.52990e12 | −0.0994681 | ||||||||
\(853\) | 2.63808e13 | 1.70615 | 0.853076 | − | 0.521787i | \(-0.174734\pi\) | ||||
0.853076 | + | 0.521787i | \(0.174734\pi\) | |||||||
\(854\) | 1.47205e13 | 0.947027 | ||||||||
\(855\) | −2.38977e13 | −1.52936 | ||||||||
\(856\) | 9.86760e11 | 0.0628173 | ||||||||
\(857\) | −2.49098e13 | −1.57745 | −0.788726 | − | 0.614745i | \(-0.789259\pi\) | ||||
−0.788726 | + | 0.614745i | \(0.789259\pi\) | |||||||
\(858\) | −1.07998e12 | −0.0680336 | ||||||||
\(859\) | 2.76464e13 | 1.73248 | 0.866242 | − | 0.499625i | \(-0.166529\pi\) | ||||
0.866242 | + | 0.499625i | \(0.166529\pi\) | |||||||
\(860\) | 7.05731e12 | 0.439943 | ||||||||
\(861\) | 1.76520e13 | 1.09466 | ||||||||
\(862\) | −4.05810e12 | −0.250346 | ||||||||
\(863\) | 6.15764e12 | 0.377890 | 0.188945 | − | 0.981988i | \(-0.439493\pi\) | ||||
0.188945 | + | 0.981988i | \(0.439493\pi\) | |||||||
\(864\) | 1.44631e13 | 0.882977 | ||||||||
\(865\) | −5.40827e12 | −0.328463 | ||||||||
\(866\) | −1.54717e13 | −0.934776 | ||||||||
\(867\) | −4.72017e11 | −0.0283708 | ||||||||
\(868\) | −1.86107e13 | −1.11282 | ||||||||
\(869\) | −1.77956e12 | −0.105858 | ||||||||
\(870\) | −2.86595e12 | −0.169602 | ||||||||
\(871\) | −1.10222e13 | −0.648915 | ||||||||
\(872\) | 1.80292e13 | 1.05597 | ||||||||
\(873\) | −2.48918e13 | −1.45041 | ||||||||
\(874\) | −1.28905e13 | −0.747252 | ||||||||
\(875\) | −4.91117e13 | −2.83236 | ||||||||
\(876\) | −4.24580e12 | −0.243608 | ||||||||
\(877\) | 1.26417e11 | 0.00721619 | 0.00360809 | − | 0.999993i | \(-0.498852\pi\) | ||||
0.00360809 | + | 0.999993i | \(0.498852\pi\) | |||||||
\(878\) | 6.48054e12 | 0.368032 | ||||||||
\(879\) | −5.92833e12 | −0.334952 | ||||||||
\(880\) | −2.84320e12 | −0.159822 | ||||||||
\(881\) | 1.81563e13 | 1.01540 | 0.507699 | − | 0.861535i | \(-0.330496\pi\) | ||||
0.507699 | + | 0.861535i | \(0.330496\pi\) | |||||||
\(882\) | −1.58195e13 | −0.880206 | ||||||||
\(883\) | −3.40979e13 | −1.88758 | −0.943788 | − | 0.330553i | \(-0.892765\pi\) | ||||
−0.943788 | + | 0.330553i | \(0.892765\pi\) | |||||||
\(884\) | −2.36635e12 | −0.130330 | ||||||||
\(885\) | 1.11244e13 | 0.609580 | ||||||||
\(886\) | −1.18270e11 | −0.00644797 | ||||||||
\(887\) | 1.64233e13 | 0.890851 | 0.445426 | − | 0.895319i | \(-0.353052\pi\) | ||||
0.445426 | + | 0.895319i | \(0.353052\pi\) | |||||||
\(888\) | −3.97633e12 | −0.214597 | ||||||||
\(889\) | −2.92518e13 | −1.57071 | ||||||||
\(890\) | −4.41039e11 | −0.0235626 | ||||||||
\(891\) | −2.44859e12 | −0.130157 | ||||||||
\(892\) | 1.71241e13 | 0.905661 | ||||||||
\(893\) | −3.76794e13 | −1.98277 | ||||||||
\(894\) | 2.71441e12 | 0.142120 | ||||||||
\(895\) | −8.82926e12 | −0.459961 | ||||||||
\(896\) | 3.05818e13 | 1.58517 | ||||||||
\(897\) | −8.48556e12 | −0.437637 | ||||||||
\(898\) | −1.06072e12 | −0.0544323 | ||||||||
\(899\) | −6.59816e12 | −0.336902 | ||||||||
\(900\) | 2.11541e13 | 1.07474 | ||||||||
\(901\) | −2.14110e11 | −0.0108237 | ||||||||
\(902\) | −4.81757e12 | −0.242325 | ||||||||
\(903\) | −6.09330e12 | −0.304970 | ||||||||
\(904\) | −1.07338e13 | −0.534560 | ||||||||
\(905\) | 4.57217e13 | 2.26571 | ||||||||
\(906\) | −2.03335e12 | −0.100262 | ||||||||
\(907\) | −3.95675e12 | −0.194136 | −0.0970679 | − | 0.995278i | \(-0.530946\pi\) | ||||
−0.0970679 | + | 0.995278i | \(0.530946\pi\) | |||||||
\(908\) | −6.26915e12 | −0.306071 | ||||||||
\(909\) | 1.40866e13 | 0.684337 | ||||||||
\(910\) | 2.44241e13 | 1.18068 | ||||||||
\(911\) | 9.23006e12 | 0.443989 | 0.221994 | − | 0.975048i | \(-0.428743\pi\) | ||||
0.221994 | + | 0.975048i | \(0.428743\pi\) | |||||||
\(912\) | −3.00207e12 | −0.143696 | ||||||||
\(913\) | 1.03377e13 | 0.492384 | ||||||||
\(914\) | −1.33772e13 | −0.634028 | ||||||||
\(915\) | 1.77394e13 | 0.836650 | ||||||||
\(916\) | −1.69312e13 | −0.794616 | ||||||||
\(917\) | 1.90140e13 | 0.887997 | ||||||||
\(918\) | −2.32400e12 | −0.108005 | ||||||||
\(919\) | −3.01409e13 | −1.39391 | −0.696957 | − | 0.717113i | \(-0.745463\pi\) | ||||
−0.696957 | + | 0.717113i | \(0.745463\pi\) | |||||||
\(920\) | 4.11753e13 | 1.89492 | ||||||||
\(921\) | −1.55953e13 | −0.714208 | ||||||||
\(922\) | −2.08194e13 | −0.948810 | ||||||||
\(923\) | 4.62245e12 | 0.209635 | ||||||||
\(924\) | 5.07465e12 | 0.229025 | ||||||||
\(925\) | −2.11504e13 | −0.949907 | ||||||||
\(926\) | −7.09682e12 | −0.317186 | ||||||||
\(927\) | 2.84708e13 | 1.26631 | ||||||||
\(928\) | 9.20882e12 | 0.407604 | ||||||||
\(929\) | 3.04484e13 | 1.34120 | 0.670601 | − | 0.741818i | \(-0.266036\pi\) | ||||
0.670601 | + | 0.741818i | \(0.266036\pi\) | |||||||
\(930\) | 8.41837e12 | 0.369024 | ||||||||
\(931\) | 5.86371e13 | 2.55799 | ||||||||
\(932\) | 1.86491e13 | 0.809629 | ||||||||
\(933\) | −1.95576e12 | −0.0844981 | ||||||||
\(934\) | −8.64049e12 | −0.371516 | ||||||||
\(935\) | 3.54228e12 | 0.151576 | ||||||||
\(936\) | −1.20162e13 | −0.511713 | ||||||||
\(937\) | 2.04000e13 | 0.864572 | 0.432286 | − | 0.901736i | \(-0.357707\pi\) | ||||
0.432286 | + | 0.901736i | \(0.357707\pi\) | |||||||
\(938\) | −1.94406e13 | −0.819967 | ||||||||
\(939\) | 2.00242e13 | 0.840543 | ||||||||
\(940\) | 5.06689e13 | 2.11673 | ||||||||
\(941\) | −2.55881e13 | −1.06386 | −0.531930 | − | 0.846789i | \(-0.678533\pi\) | ||||
−0.531930 | + | 0.846789i | \(0.678533\pi\) | |||||||
\(942\) | 6.87588e12 | 0.284511 | ||||||||
\(943\) | −3.78523e13 | −1.55880 | ||||||||
\(944\) | −4.61010e12 | −0.188945 | ||||||||
\(945\) | −6.39037e13 | −2.60665 | ||||||||
\(946\) | 1.66298e12 | 0.0675113 | ||||||||
\(947\) | 8.56722e12 | 0.346151 | 0.173075 | − | 0.984909i | \(-0.444630\pi\) | ||||
0.173075 | + | 0.984909i | \(0.444630\pi\) | |||||||
\(948\) | 2.52676e12 | 0.101608 | ||||||||
\(949\) | 1.28283e13 | 0.513420 | ||||||||
\(950\) | 2.94322e13 | 1.17238 | ||||||||
\(951\) | 2.11665e13 | 0.839146 | ||||||||
\(952\) | −9.91398e12 | −0.391185 | ||||||||
\(953\) | −3.84991e13 | −1.51193 | −0.755966 | − | 0.654611i | \(-0.772832\pi\) | ||||
−0.755966 | + | 0.654611i | \(0.772832\pi\) | |||||||
\(954\) | −4.57716e11 | −0.0178907 | ||||||||
\(955\) | −1.05528e13 | −0.410537 | ||||||||
\(956\) | −1.76991e13 | −0.685317 | ||||||||
\(957\) | 1.79915e12 | 0.0693366 | ||||||||
\(958\) | −2.08089e13 | −0.798187 | ||||||||
\(959\) | −1.11017e13 | −0.423845 | ||||||||
\(960\) | −6.19689e12 | −0.235480 | ||||||||
\(961\) | −7.05834e12 | −0.266961 | ||||||||
\(962\) | 5.05781e12 | 0.190404 | ||||||||
\(963\) | 1.42587e12 | 0.0534272 | ||||||||
\(964\) | −3.06987e13 | −1.14492 | ||||||||
\(965\) | −1.43073e13 | −0.531112 | ||||||||
\(966\) | −1.49665e13 | −0.552997 | ||||||||
\(967\) | 4.31991e13 | 1.58875 | 0.794375 | − | 0.607428i | \(-0.207799\pi\) | ||||
0.794375 | + | 0.607428i | \(0.207799\pi\) | |||||||
\(968\) | 2.13574e13 | 0.781826 | ||||||||
\(969\) | 3.74021e12 | 0.136282 | ||||||||
\(970\) | 4.65718e13 | 1.68908 | ||||||||
\(971\) | −1.97835e13 | −0.714196 | −0.357098 | − | 0.934067i | \(-0.616234\pi\) | ||||
−0.357098 | + | 0.934067i | \(0.616234\pi\) | |||||||
\(972\) | 2.07245e13 | 0.744707 | ||||||||
\(973\) | 5.76100e12 | 0.206058 | ||||||||
\(974\) | 2.83834e13 | 1.01053 | ||||||||
\(975\) | 1.93747e13 | 0.686616 | ||||||||
\(976\) | −7.35146e12 | −0.259328 | ||||||||
\(977\) | −2.56325e13 | −0.900047 | −0.450024 | − | 0.893017i | \(-0.648584\pi\) | ||||
−0.450024 | + | 0.893017i | \(0.648584\pi\) | |||||||
\(978\) | −5.78226e11 | −0.0202103 | ||||||||
\(979\) | 2.76870e11 | 0.00963281 | ||||||||
\(980\) | −7.88516e13 | −2.73082 | ||||||||
\(981\) | 2.60522e13 | 0.898119 | ||||||||
\(982\) | −4.65335e12 | −0.159685 | ||||||||
\(983\) | −3.03713e13 | −1.03746 | −0.518732 | − | 0.854937i | \(-0.673596\pi\) | ||||
−0.518732 | + | 0.854937i | \(0.673596\pi\) | |||||||
\(984\) | 1.62484e13 | 0.552499 | ||||||||
\(985\) | 6.56224e13 | 2.22121 | ||||||||
\(986\) | −1.47972e12 | −0.0498577 | ||||||||
\(987\) | −4.37476e13 | −1.46733 | ||||||||
\(988\) | 1.87507e13 | 0.626053 | ||||||||
\(989\) | 1.30662e13 | 0.434278 | ||||||||
\(990\) | 7.57254e12 | 0.250544 | ||||||||
\(991\) | −1.54521e13 | −0.508929 | −0.254465 | − | 0.967082i | \(-0.581899\pi\) | ||||
−0.254465 | + | 0.967082i | \(0.581899\pi\) | |||||||
\(992\) | −2.70498e13 | −0.886873 | ||||||||
\(993\) | −6.02910e11 | −0.0196780 | ||||||||
\(994\) | 8.15289e12 | 0.264894 | ||||||||
\(995\) | 7.98875e13 | 2.58390 | ||||||||
\(996\) | −1.46783e13 | −0.472615 | ||||||||
\(997\) | −7.77458e12 | −0.249201 | −0.124600 | − | 0.992207i | \(-0.539765\pi\) | ||||
−0.124600 | + | 0.992207i | \(0.539765\pi\) | |||||||
\(998\) | −1.37814e13 | −0.439750 | ||||||||
\(999\) | −1.32333e13 | −0.420364 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 17.10.a.a.1.4 | ✓ | 5 | |
3.2 | odd | 2 | 153.10.a.c.1.2 | 5 | |||
4.3 | odd | 2 | 272.10.a.f.1.3 | 5 | |||
17.16 | even | 2 | 289.10.a.a.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.a.a.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial | |
153.10.a.c.1.2 | 5 | 3.2 | odd | 2 | |||
272.10.a.f.1.3 | 5 | 4.3 | odd | 2 | |||
289.10.a.a.1.4 | 5 | 17.16 | even | 2 |